To find the position of an acoustic source in a room, the relative delay between two (or more) microphone signals for the direct sound must be determined. The generalized cross-correlation method is the most popular technique to do so and is well explained in a landmark paper by Knapp and Carter. In this paper, a new approach is proposed that is based on eigenvalue decomposition. Indeed, the eigenvector corresponding to the minimum eigenvalue of the covariance matrix of the microphone signals contains the impulse responses between the source and the microphone signals (and therefore all the information we need for time delay estimation). In experiments, the proposed algorithm performs well and is very accurate.

This paper introduces an efficient parameterization for the nearfield broadband beamforming problem with a single parameter to focus the beamformer to a desired operating radius and another set of parameters to control the actual broadband beampattern shape. The parameterization is based on an orthogonal basis set of elementary beampatterns by which an arbitrary beampattern can be constructed. A set of elementary beamformers are then designed for each elementary beampattern and the desired beamformer is constructed by summing the elementary beamformers with frequency and source-array distance dependent weights. An important consequence of our result is that the beamformer can be factored into three levels of filtering: (i) beampattern independent elementary beamformers; (ii) beampattern shape dependent filters; and (iii) radial focusing filters where a single parameter can be adjusted to focus the array to a desired radial distance from the array origin. As an illustration the method is applied to the problem of producing a practical array design that achieves a frequency invariant beampattern over the frequency range of 1:10 (which is suitable for speech acquisition using a microphone array), and with the array focused either to farfield or nearfield where at the lowest frequency the radial distance to the source is only three wavelengths.

A new method of profile inversion for acoustic waves propagating in a medium with spherical inhomogeneity based on the Schwinger variational method is presented. The wave equation of interest is transformed into a Schrödinger equation, so that the Born approximation and the new method could also be applied at high frequencies. It is shown that the new method is stable and is more accurate than the Born approximation. To illustrate the method, an exactly solvable analytical example is presented. Also numerical examples using synthetic data, with and without additive noise, are given and the corresponding inversion results and the stability of the method are studied.